class Solution {
    public int[][] matrixBlockSum(int[][] mat, int k) {
        int m = mat.length;
        int n = mat[0].length;
        int[][] dp = new int[m + 1][n + 1];
        for (int i = 1; i < m + 1; i++) {
            for (int j = 1; j < n + 1; j++) {
                dp[i][j] = dp[i][j - 1] + dp[i - 1][j] - dp[i - 1][j - 1] + mat[i - 1][j - 1];
            }
        }
        int[][] answer = new int[m][n];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                //+1是为了处理下标映射关系
                int x1 = Math.max(0,i - k) + 1, y1 = Math.max(0,j - k) + 1;
                int x2 = Math.min(m - 1,i + k) + 1, y2 = Math.min(n - 1,j + k) + 1;
                answer[i][j] = dp[x2][y2] - dp[x2][y1 - 1] - dp[x1 - 1][y2] + dp[x1 - 1][y1 - 1];
            }
        }
        return answer;
    }
}